I hope someone can help. I have a client who will be publishing a book and needs a cartoonist to draw various Black and White cartoons and a Book cover. The client wants a proposal of how musch I want to charge. Only problem is I've never done any book illustration. I've done greeting cards, comics and sculpture though.

Anyone have any idea on how much to charge for Cartoony B/W book drawings? Do I charge by the hour? for the Job or what?

Yeah, base the pay on how it's going to be published, or I should say, how popular the publication is. Payment can be based on many things. The last time I checked the GAG hand book of pricing, the price for a widely published color book cover was around $1200. That's not including royalties.
As Ian_Milham suggested, check out the Graphic Artists Guild handbook of pricing and ethical guide lines. A school or local library should have it if you want to browse through it. It also has sample contracts to use as well.